On the Look-Out for the Bear: Predicting Stock Market ... · minimum stock market cycle length is at least sixteen months. This is only a slight modi ca-tion of the 15-months minimum

Advanced Studies in International Economic Policy Research

Kiel Institute for the World Economy

Düsternbrooker Weg 120

D-24105 Kiel/Germany

Working Paper No. 451

On the Look-Out for the Bear:

Predicting Stock Market Downturns in G7 Countries

by

Christian Friedrich and Melanie Klein

May 2009

Kiel Advanced Studies Working Papers are preliminary papers, and responsibility for contents and distribution rests with the authors. Critical comments and suggestions for improvement are welcome.

On the Look-Out for the Bear: Predicting Stock Market Downturns

in G7 Countries∗

Christian Friedrich†, Melanie Klein‡

01.05.2009

Abstract

The paper examines the informational content of a series of macroeconomic indicator variables

with the intention to predict stock market downturns - colloquially also referred to as ‘bear

markets’ - for G7 countries. The sample consists of monthly stock market indices and a set of

exogenous indicator variables that are subject to examination, ranging from January 1970 to

September 2008. The methodical approach is twofold. In the first step, a modified version of

the Bry-Boschan business cycle dating algorithm is used to identify bull and bear markets from

the data by creating dummy variable series. In the second step, a substantial number of probit

estimations is carried out, by regressing the newly identified dummy variable series on different

specifications of indicator variables. By applying widely used in- and out-of-sample measures,

the specifications are evaluated and the forecasting performance of the indicators is assessed.

The results are mixed. While industrial production, and money stock measures seem to have

no predictive power, short and long term interest rates, term spreads as well as unemployment

rate exhibit some. Here, it is clearly possible to extract some informational content even three

months in advance and so to beat the predictions made by a recursively estimated constant.

JEL Classification:

Keywords: Bear Market Predictions, Bry-Boschan, Probit Model

∗The authors would like to thank Jonas Dovern for helpful and precious comments.†Kiel Institute for the World Economy. Email: [email protected]‡Kiel Institute for the World Economy. Email: [email protected]

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1 Introduction

The recent financial turmoil has caused a full-blown economic crisis with severe output losses and

alongside resulted in extensive stock market downturns for G7 countries. The Dow Jones Industrial

Average for instance fell by 35 percent during January 2008 and January 2009. The experiences for

other advanced economies are similar. At a point like this, routinely the question is asked, whether a

stock market downturn could have been avoided or at least foreseen in an earlier stadium. Interest in

answering this question is spread over various professions and interest groups - the most prominent

ones include: Scholars that are active in the fields of forecasting and finance, policy makers that

could ease monetary or fiscal policy early enough to ensure that their impact facilitates the downturn

in time and last but not least it also is in the interest of investors to reallocate their portfolios some

time in advance - either to another country or to another asset class.

Hence, the question this paper addresses is whether it is possible to predict stock market down-

turns - colloquially also referred to as ‘bear markets’ - or at least to identify some hints to be more

attentive than usual. Although predicting stock market returns is a difficult business1, and being

overly successful in it would result in everything but an academic piece of work, it could never-

theless be possible to identify some potential harbingers - such as early reactions by the monetary

authority or actions taken by companies in financial distress - that frequently precede a stock market

downturn.

The methodical approach we apply consists of two steps. In the first step, a modified version

of the Bry-Boschan business cycle dating algorithm is used to identify bull and bear markets from

the data by creating dummy variable series.2 This approach was first applied to the stock market

by Pagan and Sossounov [2003] in 2002 and subsequently adopted by Biscarri and Perez de Gracia

[2002], Gonzalez et al. [2005] and Cunado et al. [2008]. In the second step, we carry out a sub-

stantial number of probit estimations, by regressing the newly identified dummy variable series on

different specifications of macroeconomic indicator variables. When applying widely used in- and

out-of-sample measures, we are then able to evaluate the specifications and to assess the forecasting

performance of the selected indicators. We use G7 market data since the recent crisis has emerged

in the industrialized world and the high volumes of stocks traded within these countries make this

sample more relevant to investors. Furthermore, a good data quality and broad availability enables

us to use a sample that for most countries is dating back to the beginning of the 70ies.

1However, there is a wide range of empirical literature e.g. Campbell [1985], Chen et al. [1986], Lewellen [2004],Rapach et al. [2005], Campbell and Yogo [2006], Bekaert and Ang [2007].

2A different approach to identify the bear markets is the application of regime switching models, e.g. used byMaheu and McCurdy [2000], Ang and Bekaert [2002], Chen [2009]. Prejudicially for our investigation would be thatthese models do not date the phase of the cycles.

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Even though the objective of this paper is not the prediction of the stock returns but the

prediction of the bear markets, both approaches are similar as well as the selection of the independent

variables. So far, the following macro variables have been investigated and are also partly included

in our model. Having a look first on the money stock, Keran [1971] pointes out that monetary

actions, measured by changes in the money stock, have no direct impact on stock prices. Instead,

it occurs through their effect on inflation and corporate earnings expectations (For further readings

see Fama [1981], Pearce and Roley [1983], Kaul [1987], Thorbecke [1997] among others). Regarding

the evaluation of the interest rates, Keran [1971] also emphasizes that this measure is a reasonably

good empirical explanation of stock price movements. Chen et al. [1986], who investigate nine macro

variables regarding their impact on pricing of stocks, conclude that interest rates - the authors include

the term structure as difference between the long-term government bonds and the treasury bill - as

well as industrial production and changes in the risk premium are significant in explaining expected

stock returns. Rapach et al. [2005] who tested for 12 industrialized countries the predictability of

stock returns showed also a high forecast ability of interest rates across countries. But in contrary to

Chen et al. [1986], who focused on the US market, their results concerning the industrial production

and the unemployment rate are not so clear, and though depending on the country (See also for

readings on industrial production and unemployment rate: Balvers et al. [1990], Boyd et al. [2001]).

The approach to identify and analyse recessions in the first part of this paper is adopted from

Biscarri and Perez de Gracia [2002] and Cunado et al. [2008]. We expand their examination by in-

creasing the number of countries and by carrying out in-sample and out-of-sample probit regressions

with the objective to forecast bear markets, whereby the selection of the indicators was influenced

by the results of the investigations on stock return predictability. Hence, our overall approach is

similar to Chen [2009] who used in contrast to our paper a Markov-switching model for identifing

the recession periods in the stock market and who just focused on the US market. His main findings

are that term spread and inflation are the most useful predictors of downturns in the US stock

market. Furthermore, Chen [2009] concludes when comparing the forecast ability of macroeconomic

variables that they have higher explanatory power regarding the prediction of bear markets than of

stock returns.

The remainder of this paper is organized as follows. Section 2 is primarily focusing on the

modification of the Bry-Boschan business cycle dating algorithm to financial market environment and

its application to the stock market index series. As a second task, the hereby obtained identification

results undergo a first analysis and thirdly, a selection of stylized facts on bear markets is presented.

Section 3 represents the core of the paper and contains the theoretical background for the probit

estimations, the estimation results for the in- and out-of-sample case as well as a number of evaluation

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measures to identify the most promising specifications. Section 4 concludes.

2 Identifying Bear Markets

2.1 Empirical Methodology: The Bry-Boschan Algorithm

Before turning to a detailed description of the dating algorithm applied, some definitions are made.

As stated in the introduction, we define bear (bull) markets as those phases of the stock market

index series that exhibit a prolonged downward (upward) movement, however such parts can be

interspersed with sporadic upward (downward) movements. Each phase is located between two

turning points, whereas the starting point of a bear (bull) market is referred to as a peak (trough)

and the ending point as a trough (peak). Finally, two phases in a row - i.e. the distance between

two troughs or two peaks respectively - constitute a cycle.

The Bry-Boschan’s business cycle dating is based on an algorithm created by Bry and Boschan

[1971] that identifies the location of turning points in the logged GDP series. As stated above,

in this paper, we apply a modified version developed by Pagan and Sossounov [2003] that adjusts

the original algorithm to the needs of (logged) stock market index series. This modified algorithm

divides each country’s stock market index in bear and bull market phases by creating a dummy

variable series that takes on the value 1 in case of a bear market and 0 in case of a bull market. In

the remainder of this text, we refer to this series as the ‘bear market series’.

The modified algorithm consists of several sub-procedures that are applied to the stock market

series. The most important ones are presented in the following:

• The main procedure is based on a symmetric sixteen months (i.e. eight months in both

directions) moving average filter that is used to derive an upper and a lower bound series

to the observed stock market index series. Hereafter, the points of tangency of the stock

market index series and the upper bound series become the initial location for peaks, whereas

the points of tangency with the lower bound series become the algorithm’s first guess for

troughs. The corresponding filter procedure in the original algorithm generated symmetric

one year (i.e. six months in both directions) moving averages and is part of a series of filter

procedures that smooth the observed data several times. To avoid losing the informational

content incorporated in outliers, which is of high relevance in the context of stock market data,

the modified version only contains the above mentioned sixteen months filter procedure.

• After the initial location of peaks and troughs, a procedure called ‘alternate’ is launched to

ensure that peaks and troughs occur consecutively. In the beginning, a step function that

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increases by a constant margin when a new peak is reached is generated. Thereafter, the

lowest trough within each step (i.e. between two peaks) is identified and kept, while all other

troughs in this interval are deleted from the set of potential troughs. By applying an analogous

approach to the troughs and creating a second step function, the highest peaks within two

troughs are kept and all others are eliminated. As stated above, this procedure ensures that

peaks and troughs alternate and is therefore repeated after every change made to the series.

• The next two procedures are concerned with the enforcement of minimum distance require-

ments for the location of turning points. The so called ‘mincycle’ procedure ensures that the

minimum stock market cycle length is at least sixteen months. This is only a slight modifica-

tion of the 15-months minimum length criterion in the original algorithm for business cycles.

This procedure works as follows: First, all turning points are extracted in a separate series.

When all adjacent peaks (or troughs respectively) exhibit a higher distance than the minimum

cycle length, both peaks (troughs) are kept and the program continues. In case this rule is vi-

olated, the mincycle procedure deletes the lowest of the two problematic peaks (or the highest

of the problematic troughs respectively) before moving on.

• The second distance requirement procedure - the so called ‘minphase’ procedure - is targeted

at the enforcement of the minimum phase length. Latter one is set to four months in the stock

market context, which is one month less than in the original algorithm. Another modification is

given by the introduction of a ‘20 percent criterion’: Since according to Pagan and Soussonov,

a significantly lower minimum phase requirement would produce spurious cycles, the authors

include the criterion that sharp market movements in either direction overrule the minphase

requirement. The minphase procedure works similar to the mincycle routine depicted above:

1. The turning points are extracted in a separate series again.

2. The distance between two adjacent turning points (note the difference to the mincylce

procedure) is compared with the minimum requirement. If the latter one is not violated,

all turning points are kept and the overall program continues.

3. In any other case, the problematic location is tested for eligibility of the 20 percent

criterion. The latter one is defined as a cumulated change in logged stock prices of more

than 20 percent in less than four months.

4. When the location is eligible for the 20 percent criterion, both turning points are kept and

the program continues, whereas in any other case, the program deletes the first turning

point before moving on.

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The modified algorithm itself produces two dummy variable output series. A first series takes on

the value of one when a peak is identified and generates a value of zero elsewhere. A second series

indicates the locations of all troughs in an analogous manner. Furthermore, there are additional

procedures that are used to refine the endpoints after the moving average filter has been applied, to

display the results after the identification has been carried out, and finally a procedure that converts

the generated (peak- and trough-) dummy variable series in the above defined ‘bear market series’.

While the former dummy variable series took on the value of one only on their respective turning

points, the latter one - the bear market series - takes on the value of one during the bear market

phases (and zero elsewhere).

Pagan and Sossounov mostly reason out the adjustments they made by citing from the so called

‘Dow Theory’, which was propagated by Charles Dow in the early 20th century. According to the

authors, this strand of literature introduces the notion of ‘bull and bear markets’ and defines them

formally with a set of general figures based on the market commentators experience at that time.

2.2 Data

Using MSCI stock price indices, we apply the previous algorithm and the subsequently described

probit estimations to the G7 countries, which are: Germany, France, Italy, US, UK, Canada and

Japan. Since the MSCI index, which is available from 1969 onwards, is published on daily basis,

we extracted the last day of the months as proxy for the monthly price index over a period from

January 1970 to October 2008. In addition, the natural logarithm of the stock prices is used for the

identification of the starting and ending points of the bull and bear markets.

For further investigations on the predictability of bear markets, we decided to choose eight

macroeconomic variables in monthly frequency based on previous results in the literatur. In effort

to have better time-series properties, the first four of the following variables are included in the

model as growth rates. The indicator variables we consider are:

• industrial production growth (the first difference in the log-levels of the industrial production

index, PROD);

• inflation rate (the first difference in the log-levels of the consumer price index, CPI);

• narrow money growth (the first difference in the log-levels of the money stock M1);

• broad money growth (the first difference in the log-levels of the money stock M2);

• 3-month interbank rate (IB);

• 10-years government bond yield (GB);

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• term spread (the difference between the 3-month interbank rate and the 10-years government

bond yield, SPREAD);

• unemployment rate as percentage of the civilian labour force (UNEMP).

The sample was intended to cover the time from January 1970 to September 2008. However, for

some variables particular periods were not available:

1. UNEMP for Italy (only available from November 1979 to July 2008), France (January 1978)

and the UK (Dezember 1970);

2. the money stock M1 for Italy (first available in January 1980) and France (December 1977);

3. the money stock M2 for the UK (July 1982), France and Italy (January 1980)

The data is obtained via Datastream.

2.3 Identification Results

2.3.1 Turning Point Analysis

The following chapter analyses the results obtained through the application of the Bry-Boschan

business dating algorithm to the sample countries. Over the time period 1970 - 2008, we obtained

a large number of turning points (around 20 per country). In the following, we enlarge on the most

important bear markets (peak −→ trough) in recent history, and furthermore explain their impacts

on the seven countries in greater detail.

Table 1: Correlation matrix for the MSCI series of all countries

Germany France Canada Japan US UK ItalyGermany 1France 0.98 1Canada 0.95 0.91 1Japan 0.48 0.61 0.5 1US 0.98 0.97 0.93 0.54 1UK 0.98 0.97 0.95 0.54 0.99 1Italy 0.97 0.97 0.93 0.59 0.98 0.99 1

Before looking at the graphs of figure 1, it is interesting to see the correlations between the

seven MSCI series (see table 1).3 The most striking feature of this table is that the correlations

between all countries are very high with the exception of Japan which exhibits strong lower values.

Furthermore, Canada shows slightly less correlations to the other European countries and to the

US.3Mean and standard deviations of the series can be found in the appendix (table 10).

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Figure 1: Log stock prices 1970/01-2008/10 (MSCI series are in the domestic currency)

USA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20064.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

United Kingdom

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20063.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

Canada

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20064.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

Japan

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20064.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

Germany

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20064.0

4.5

5.0

5.5

6.0

6.5

7.0

France

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20064.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

Italy

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20063.5

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

In the following we concentrate on three key occasions between 1970 and 2008 - for two of them

the US market was the trigger. The first phase is the time period of the seventies. The origin for

the bear market - it began first in Germany (1972:07) and Great Britain (1972:8) followed by the

US in December 1972, Japan (1973:01), France in April, Italy in June and Canada in October - was

the first oil crisis in 1973 and the dissolving of Bretton Woods between 1971 and 1973. The former

was caused by an oil embargo of the OPEC as protest against the US support of Israel during the

Yim-Kuppor War. Even though only France, the Netherlands and the US were affected directly by

the embargo, the other countries were afflicted with the extreme rising oil price. During the war

in 1973 the oil price increased from $18 to approximately $41 per barrel and rose to the pike of

$106 in April 1979 (Datastream). Compared to the first oil crisis, the second one in 1979 had not

such strong negative implications on the stock prices. In contrast, Canada’s and Italy’s stock prices

increased since 1978 and found their peaks in 1981, the highest values since 1970. Observing the

seventies, Canada, Japan and Germany suffered less compared to the rest and underwent only a

‘mild’ downturn as reflected by their losses during the bear market of the first oil crisis. Germany’s

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index value decreased by 10.1 percent during its downturn, going from 1972:07 to 1974:09, followed

by Canada and Japan which lost 10.8 and 10.3 percent respectively, even though Canada underwent

the shortest contraction phase between the seven countries with 11 month (from 1973:10 to 1974:09).4

An explanation for this finding could be that Canada as a net exporter of oil is largely independent of

the world oil supply. To find conclusive reasons for Japan’s low sensitivity during this time, it is more

concealed. A feasible explanation is its relative isolation from Europe, in 2007 only 14.8 percent of

Japan’s exports and 10.5 percent of Japan’s imports were traded with the EU-27. Its main trading

partners are the US and Asian countries. The second one could be its strengthened export sector

which turned the trade balance in a surplus since 1965 and thus made the Japanese economy more

robust.5 Approximately in the beginning of the eighties, the stock prices of all countries recovered

their initial level of the time before the first oil crisis, likewise Italy which has spent 54 month - the

longest contraction phase within the whole analysis - in this bear market (1973:06 - 1977:12).

The second noticeable trough is identifiable through the strong fall in the stock index in the last

two month of 1987 (see figure 1). Starting on October 19th 1987 in the US, known as the ‘Black

Monday’, the crash spread fast to the UK, Canada, Japan, followed by Germany, France and Italy.

During this day in October, the Dow Jones Industrial Average fell by 508 points and caused the

biggest crash on a single day in the history of the NYSE.6 The distinctive characteristics of this

bear market are: 1) it was short and 2) the level of per month losses is significantly higher than

during the other bear markets, especially in the US and UK. In this second contraction phase two

groups emerged, excluding Japan. The first one with the US, UK and Canada show a very short

bear market (four, three, and five months) with similar losses. The stock market index decreased

by 6.7 percent in the US,UK and 5.5 percent in Canada. On the contrary within the second group

including Germany, France and Italy the markets are longer (21, 17, and 21 months) and the losses

are higher (Germany 13.1 percent, France 10.3 percent, Italy 9.2 percent). Examining the per month

losses the picture is different. The US with 1.7 percent and the UK with 2.2 percent show the highest

monthly loss between 1970 and 2008.

The third downturn was initiated by the bust of the dot-com bubble whereas in the US the

crisis were precipitated. A special characteristic for this downturn are a uniform phase length and

a low level of monthly losses across all countries. Certainly, the incident on September 11th 2001

4The residual losses per country are (the length of the bear market is in bracket): US 15.9 percent (21 months),France 18.6 percent (17 months), UK 31.2 percent (27 months), Italy 29 percent (54 months).

5The exports grew from 1965 to 1975 by 81.7 percent (Datastream).6This crash was generated on the one hand through economic factors and on the other hand through technical

and systemic problems. The former included among others a weak dollar, fear of inflation and a rapid growing of theAmerican trade deficit. The latter problem was dominated by the former stock trading system. The trading pensumin these days was overwhelmed and could not be executed, in particular without internet and with the technology(e.g. computers) at that time. For further readings: Samuelson [2007].

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was a strengthened effect which extended the bear market phase. Starting around the turn of the

millennium and ending in early 2003, the average duration was 32 months. The losses per month

varied between 0.2 and 0.6 percent (US: 0.33, UK: 0.2, Canada: 0.4, Japan: 0.3, Germany: 0.6,

France: 0.4, Italy: 0.4). Another time Japan is a special case. It also underwent this bear market

with approximately 37 months and a per month loss of 0.3 percent but did not experience the

consistently increasing trend during the nineties compared to the other six countries. Slumping in

its so far biggest economic crisis in 1990, whereby the downtrend of the stock prices began, the

Japanese MSCI index has not recovered its value of 1990 up to now.

2.3.2 Stylized Facts on Bear Markets

After the peaks and troughs of the seven countries have been identified, we analyze the main

characteristics of their bear markets. For this purpose we consider five properties:

1. The average duration of the bear markets (Duration).

2. The average amplitude of the markets for each country (Amplitude). This measure is defined

as the percentage change of the log stock prices from one turning point to the following.

3. The approximation for the cumulative movements of the stock prices within the phase from

peak to trough, relatively to the previous peak (Cum. movements).

4. The shape of the bear market, in particular the divergence from a triangle. Comparable to

Pagan and Sossounov [2003], we will refer to this as the ‘excess’ index.

5. The last value is the percentaged fraction of all contractions, that exhibited a reduction of

more than 20 percent between two turning points (Change ≥ 20 % ).

The initial point for these calculations is the computation of a dummy variable Bt, which turns one

when the stock market is in a recession and takes on the value zero when the stock market follows

an expansion phase. Having this, the total time spent in an bearish market is∑T

t=1 Bt. Calculating

the number of troughs:

NT =T∑

t=1

Bt(1 − Bt+1) + 1 (1)

and dividing this value by the time being in a bear market, yields the average duration of the

contraction phases per country.

For a better understanding, figure 2 plots a stylized bear market with point A being a peak

and C symbolizing a trough. If indeed the shape of a bear market follows a triangular, the data

generating process is a random walk. Thus the best prediction for the next period would be the

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Figure 2: Stylized Bear Market

current stock price, which implies that in this case a forecast by exogenous variables should show

worse results.

Based on the fact that the height of the triangle is the amplitude and the duration is part of the

hypotenuse, the area of the triangle and so an approximation to the cumulative movements in the

stock prices within the phase peak-trough must be:

Cumi = 0.5(Duri · Ampi) (2)

Because this triangle just drafts the real aspect of a bear market and it might be that the Cumi

differs from the actual cumulative movements, Ci. Thus the ‘excess’ index is needed, since the actual

path through the phase may not be well approximated by a triangle, which is:

Ei = (Ci − 0.5Ampi − Cumi) · Duri (3)

To obtain the figure Ci per country, the numbers in the series of the log stock prices for the

bear markets (the prices during the bull markets are set to zero) are added one after the other.

Furthermore, we divided the sum of the resulting series by the number of troughs.7

Table 1 gives the results of these measures for the G7 countries. The first four rowes are targeted

on evaluating the shape of the bear markets, while the last two values are measures for stock market

volatility. By looking at the average duration of the bear markets, it is striking that in five cases -

with the exception of Canada and Italy - the corresponding values lie between 14 and 19 months.

This result is quite close to the claim of Hamilton in 1921, who assumed that over a period of 25

years the bear markets last on average 17 months (Rhea [1932] p37). Italy exhibits the largest bear

markets with a duration of 22 months and an average capital loss of 54 percent. As a next measure,

the cumulated movement values are calculated. While the values themselves have no interpretation,

7For a more detailed description and the underlying formulae see Pagan and Sossounov [2003] andBiscarri and Perez de Gracia [2002].

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they are needed to derive the excess index, which in turn contains some interesting information.

Based on the excess index values in table 1, the bear markets of Japan, Italy and the UK differ

significantly from the triangular shape. Thus it might be possible to predict their recessions using

macroeconomic indicator variables. The trend of the deviation from the stylized bear market is also

noted by Pagan and Sossounov [2003] and Harding and Pagan [2002]. The former emphasize that

for their sample period from 1945 to 1997 this behaviour became more emphatic over time for the

US stock market. The last variable in the table proves that the decision to include the 20 percent

criterion during the Bry and Boschan identification process was needed. All countries show a high

number whereas the UK outperforms the rest.

Table 2: Bear market characteristics for all countries

Germany France Canada Japan US UK ItalyDuration 15 14 11 19 15 17 22Amplitude (in percent) -30 -45 -31 -41 -36 -55 -54Cum. movements -2.11 -3.09 -2.05 -4.80 -3.09 -4.00 -7.48Excess index(in percent) 1.22 2.1 -1.19 -3.39 -1.7 5.01 -5.38Volatility 0.53 0.72 0.45 0.83 0.68 0.86 1.13Change (in percent) ≥ 20 % 50 63 55 60 50 100 80

Finally, compared to Biscarri and Perez de Gracia [2002], our index for volatility turns out to

be much higher. In their analysis, Italy exhibits a value of only 0.85 for the period from 1957 to

1998. Although this difference is significant, Italy is the most volatile market in their sample as well.

Furthermore, as indicated by table 1 and noted by Biscarri and Perez de Gracia [2002] as well, the

longer the duration and the higher the amplitude are, the higher is the volatility during the bear

markets.

3 Predicting Bear Markets

3.1 Empirical Methodology: The Probit Model

A probit model is a regression model that contains a dependent variable which lies strictly between

0 and 1 and hence can be interpreted as a probability. The population probit model is given by

Pr(Y = 1|X1, X2, ..., Xk) = Φ(β0 + β1 · X1 + β2 · X2 + ...βk · Xk) (4)

where Xk are the regressors, βk are the corresponding probit coefficients, and Φ is the cumulative

standard normal distribution.8 Since the probit coefficients are difficult to interpret, usually the

8See any standard textbook for econometrics: e.g. Stock and Watson [2008] p. 392.

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predicted probabilities - i.e. the fitted values of the estimated model - are calculated based on the

earlier obtained coefficients.

In our analysis, the dependent variable is given by the bear markets series - i.e. the series that

was obtained previously by applying the modified Bry-Boschan business cycle dating algorithm to

the stock market index series - and the exogenous variables are represented by indicator variables

that are assessed for their forecasting power. Since forecasting stock market returns is a tedious

business, we apply a huge variety of specifications. To structure our approach in the most traceable

way, we first create a unified framework that contains a large number of specifications and modify

it several times. The structure of this framework is the following:

In the first specification for each country, we include the first 12 lags of all indicator variables.9

We do not include any contemporary values, since they are not available at the time the forecast

is made. In the second specification, we again include the same number of lags for all indicator

variables. But now, we apply a selection procedure to the regression output that eliminates all

insignificant regressors and re-estimates the model until all regressors are significant at the 10 percent

level at least. The following 16 specifications are based on an analogous framework but on a rather

disaggregated level. The bear market series is now regressed on the first 12 lags of each of the eight

indicator variables. Hereafter, the aforementioned selection procedure is applied again and the bear

market series is regressed only on the significant lags of each of the indicator variables.

Before turning to the variations of the above depicted framework, a brief introduction into the

most prominent evaluation concepts of forecasting models is presented: The ‘in-sample’ and the ‘out-

of-sample’ analysis. The in-sample analysis serves as a preliminary assessment of the forecasting

performance of indicator variables. The defining characteristic of the in-sample analysis is that each

specification is estimated over the whole sample range. Since all available observations are used

to estimate the model, no data points are left to evaluate the predictions made. This drawback

is resolved by conducting an out-of-sample analysis. Here, the sample is divided into two parts.

Whereas the first part of the sample (initial estimation sample) is used to estimate the model from

the data on the exogenous variables and the second part (out-of-sample period) is used to evaluate

the models predictions against the actual realizations of the dependent variable - in our case, the

bear markets series. Since the exogenous variables are unkown at the time the forecast is made,

the out-of-sample analysis should be consulted to evaluate the forecasting performance in the first

place (Ashley et al. [1980], Meese and Rogoff [1983]). In setting up the out-of-sample analysis, it is

crucial to decide on how the out-of-sample values are generated. They can be obtained by either a

rolling window scheme that contains a fixed number of observations and is moved forward over time

9In the first two specifications, we exclude the SPREAD variable. Since including it together with the utilizationof its defining interest rates would result in perfect multicollinearity.

13

or by a recursive estimation scheme, where the initial estimation sample is increased by a specific

number of observations each period. In this paper, we apply the latter approach with one step ahead

forcasts each period.

Having this in mind, we continue with a description of the cases in which the specification

framework or its modifications are used: Firstly, the framework is applied as described above and

serves as the baseline set-up for the in-sample analysis. Secondly, when turning to the out-of-sample

analysis the lag length is increased to three which serves as the new baseline. Finally, by modifying

the starting point of the evaluation period - i.e. the point where the out-of-sample forecast starts -

a third and fourth modification is generated.

To systematically evaluate the large number of estimation results, we employ measures that are

frequently used in the forecasting literature to assess the prediction power of indicator variables.

But before turning to the description of more sophisticated measures, a fairly simple method of

examination should be mentioned. As a first approach, the predicted probabilities are plotted

against the time. When, in addition, the earlier obtained bear market series is added to the graph,

a first visual impression of the models’ forecasting power is gained. Especially models that perform

particularly poor in this exercise can be identified at an early stage.

Although it only can be applied to the in-sample case, the so called pseudo R2 is a second

measure to evaluate probability forecasts (Estrella and Mishkin [1998]). It has to be calculated

seperately for each specification via the following formula:

psR2 = 1 − (LLu

LLc)−2/T ·LLc (5)

where LLu denotes the log-likelihood of the unconstrained model and LLc denotes the log-likelihood

of the constrained model (i.e. the constant only). The values of the pseudo R2 range between 0 and

1, where a higher value indicates a better fit.

The evaluation measures number three and four are the Quadratic Probability Scores (QPS)

as suggested by Brier [1950] and the Logarithmic Probability Scores (LPS), both calculated on

basis of the predicted probabilities and can be used for assessing the in-sample and out-of-sample

results. The QPS is obtained by calculating two times the sum of the squared differences between

the predicted probabilities and the realizations of the bear market series and dividing the result by

the sample size. The entire formula is given by:

QPS =1

T·

t−1∑

T

2 · (Pt − Rt)2 (6)

where Pt denotes the probability forecast for time t and Rt denotes its ex-post realization. The fit

14

of the model is high, when the QPS takes on a small value. In similar fashion, the LPS can be

computed:

LPS = −1

T·

t−1∑

T

(1 − Rt) · ln(1 − P ) + Rt · ln(Pt) (7)

where Pt denotes the probability forecast made for time t and Rt is the realization of the corre-

sponding sample point. The lower bound of both measures is 0 and indicates the highest model

fit.

To effectively evaluate a specification of interest with the last two measures, a benchmark model

is derived. For both the in-sample and the out-of-sample case, such a benchmark is given by

a constant-only-specification that is evaluated by QPS and LPS as well. In the in-sample case,

the constant is represented by the average value of the dependent variable calculated over the

whole sample range. In the out-of-sample case, the constant is obtained by a stepwise determined

dependent variable average over the estimation period - starting with the initial estimation sample

average and increasing its range by one oberservation in each of the following periods. As a rule of

assessment, it can be stated that as long as the specification of interest produces a lower QPS or

LPS than the benchmark model, the indicator variables of the specification exhibit some forecasting

power and thus, the model is helpful in predicting bear markets.

To formally assess the significance of the difference between the proposed forecasting model

and the benchmark constants, a series of Diebold-Mariano tests is applied (Diebold and Mariano

[1994]). These tests are conducted in two versions. Firstly, the null hypothesis that the foreceasting

model is as good as the constant is tested against the alternative hypothesis that the forecasting

model performs signifcantly better. Secondly, the opposite case is considered as well with the null

stating that both models are equal and the alternative that the constant model performs better.

Since both cases usually yield the same results, we only report the more interesting first case. The

Diebold-Mariano test is evaluated by its p-value, indicating a rejection of the null - i.e. stating that

the forecasting model performs significantly better - by a p-value smaller than five percent.

3.2 Estimation Results

The presentation of the results is divided into three parts. Firstly, we examine the fit via an in-sample

analysis. Secondly, we assess the prediction power of the indicator variables by running the out-of-

sample analysis. Thirdly, we carry out a large number of robustness checks for the out-of-sample

case.

15

3.2.1 In-Sample Analysis

As stated above, the in-sample analysis serves as a preliminary assessment of the indicator variables’

forecasting performance and is entirely based on an ex-post perspective. Hence, the specifications

are estimated over the maximum sample range and the minimum lag length is chosen abitrarily. For

Canada, Germany, Japan, and the US where data is available over the whole sample, the estimation

is carried out from January 1970 to September 2008. Since the data on indicator variables for

France, Italy, and the UK is not entirely available from January 1970 onwards and for each of these

three countries at least one indicator series starts not before the late 70ies, we set their in-sample

start to January 1980. Furthermore, the sample for Italy ends due to a lack of recent unemployment

data already in June 2008.

As already mentioned in subsection 3.1., we first estimate the baseline set-up for each country,

starting with a minimum lag length of one. After having obtained the coefficients, the predicted

probabilities can be calculated. Plotted against the time and supplemented by the bear market

series, these predicted probabilities generate a first impression of the model fit (see figure 3). At a

first glance a number of bear markets were predicted fairly well (e.g. 1973 in Japan, 1986/7 in the

US, 1994 in Italy and the UK and after 2000 in Germany and France). By contrast, e.g. the predicted

probabilities in the case of Canada from 1991 onwards, rather seem to fluctuate independently of

the earlier identified bear markets series.

As a typical in-sample measure, the pseudo R2 is applied next to evaluate the different spec-

ifications (see table 3). The results indicate that the specifications with the highest pseudo R2

and hence, the highest prediction power relatively to the constant-only-case, are obtained when all

variables are included. The resulting pseudo R2 values are different across countries and range from

a low 0.26 for Canada to a high 0.65 for France. When in addition, the lag selection procedure is

applied to the all-variable model for each country, slightly smaller values are obtained. This stems

from the fact that the pseudo R2 does not include a correction term for the number of regressors

included in the model and hence, the model with the higher number of regressors is always found

to be better.

In a next step, the forecasting performance of the single variable predictions is examined. The

values of the pseudo R2 are mostly located in the range between zero and small double digit values

which is significantly lower than in the all-variable case. This finding indicates that no single

variable has the prediction power to compete with the whole set of variables. However, it rather can

be infered that PROD and M1 have a low informational content, especially when the lag selection

procedure is applied and basically for most countries all lags of these two variables are thrown

out. A similar case is stated for the pseudo R2 values of M2 and CPI, but their after-lag selection

16

Figure 3: In-sample recession probabilities - all variables - 1 lag

Germany

1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 20070.00

0.25

0.50

0.75

1.00

France

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20060.00

0.25

0.50

0.75

1.00

Canada

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20060.00

0.25

0.50

0.75

1.00

Japan

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20060.00

0.25

0.50

0.75

1.00

USA

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20060.00

0.25

0.50

0.75

1.00

United Kingdom

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20060.00

0.25

0.50

0.75

1.00

Italy

1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 20060.00

0.25

0.50

0.75

1.00

Note: shaded part = actual bear markets; plotted line = fitted values of the probit estimation. The time period for thein-sample analysis of France, the United Kingdom and Italy starts in January 1980.

procedure specification includes a positive number of regressors. Better prediction qualities seem to

be incorporated in the interest rate variables, such as GB, IB and SPREAD. Here, the pseudo R2

values are frequently located in the lower two-digit range, such as 0.1 to 0.2, without any notable

reduction when the lag selection procedure is applied.

In general, when the Quadratic Probability Scores (QPS) and Logarithmic Probability Scores

(LPS) are examined a similar picture emerges (see table 4 and 5). Here, the figures from the first 18

columns are evaluated against the scores of the constant in column 19. As soon as the QPS or LPS

values of an indicator variable specification is smaller than the QPS or LPS values of the constant,

the respective specification can be seen as useful for prediction. The all-variable specification again

has the highest prediction power across all countries - with all indicator values clearly being lower

than the values of the constants.

Extending the country analysis to the single indicator variable case, the best predictions can be

made for Japanese stock market downturns - here, basically every variable beats the constant. The

17

Table 3: In-sample results - pseudo R2 - 1 lag

All variables PROD CPI M1 M2N S N S N S N S N S

Germany 0.38 0.30 0.03 0.00 0.12 0.10 0.04 0.00 0.02 0.00France 0.65 0.54 0.05 0.00 0.10 0.09 0.02 0.00 0.05 0.03Canada 0.26 0.16 0.02 0.00 0.03 0.02 0.04 0.03 0.04 0.03Japan 0.28 0.19 0.09 0.03 0.08 0.06 0.10 0.10 0.12 0.09USA 0.36 0.31 0.05 0.03 0.07 0.07 0.08 0.07 0.06 0.05UK 0.48 0.31 0.07 0.00 0.08 0.02 0.07 0.00 0.17 0.15Italy 0.34 0.23 0.05 0.00 0.07 0.00 0.07 0.00 0.05 0.00

IB GB SPREAD UNEMPN S N S N S N S

Germany 0.15 0.14 0.15 0.14 0.11 0.07 0.14 0.12France 0.12 0.11 0.18 0.18 0.04 0.02 0.19 0.18Canada 0.06 0.04 0.09 0.08 0.06 0.05 0.05 0.02Japan 0.14 0.13 0.10 0.09 0.09 0.08 0.07 0.01USA 0.05 0.03 0.05 0.02 0.06 0.02 0.05 0.05UK 0.11 0.07 0.13 0.12 0.12 0.09 0.10 0.07Italy 0.09 0.08 0.16 0.16 0.11 0.10 0.06 0.01

Note: ‘N’, ‘S’ are non-selected and selected. In the selected estimation are thesignificant parameters of the 12 lags non-selected estimation included.

Table 4: In-sample results - QPS - 1 lag



IB GB SPREAD UNEMP ConstN S N S N S N S

Germany 0.38 0.38 0.37 0.38 0.39 0.40 0.39 0.39 0.43France 0.30 0.30 0.28 0.28 0.31 0.32 0.25 0.25 0.32Canada 0.37 0.37 0.36 0.36 0.37 0.37 0.38 0.38 0.39Japan 0.45 0.45 0.47 0.47 0.47 0.47 0.48 0.48 0.49USA 0.46 0.46 0.46 0.47 0.45 0.46 0.46 0.46 0.47UK 0.34 0.34 0.33 0.33 0.33 0.33 0.34 0.34 0.36Italy 0.46 0.47 0.43 0.43 0.45 0.46 0.48 0.48 0.49

Note: ‘N’, ‘S’ are non-selected and selected. In the selected estimation are thesignificant parameters of the 12 lags non-selected estimation included. ‘Const’ isthe Constant which is used as a benchmark for evaluating the forecasting abilitiesof the exogenous variables.

lowest number of indicator variables that exhibit prediction power are found in the case of Canada

and to some lower extent also for Germany and the UK. But nevertheless, even for Canada, more

than half of the indicator variables have a QPS and LPS that beat the corresponding measures of

the constant.

18

Table 5: In-sample results - LPS - 1 lag





Note: ‘N’, ‘S’ are non-selected and selected. In the selected estimation are thesignificant parameters of the 12 lags non-selected estimation included. ‘Const’ isthe Constant which is used as a benchmark for evaluating the forecasting abilitiesof the exogenous variables.

Table 6: Diebold Mariano Test of the in-sample results - 1 lag (p-values)


Germany 0.00 0.00 0.36 0.50 0.00 0.00 0.08 0.50 0.39 0.50France 0.00 0.00 0.86 0.90 0.80 0.47 0.97 0.89 0.42 0.74Canada 0.00 0.00 0.11 0.50 0.12 0.17 0.04 0.13 0.07 0.11Japan 0.00 0.00 0.03 0.21 0.08 0.38 0.01 0.01 0.00 0.01

USA 0.00 0.00 0.02 0.07 0.00 0.01 0.00 0.00 0.02 0.02

UK 0.00 0.00 0.58 0.51 0.88 0.82 0.26 0.14 0.38 0.88Italy 0.00 0.00 0.09 0.92 0.10 0.27 0.07 0.17 0.46 0.92


Germany 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

France 0.05 0.04 0.01 0.01 0.39 0.44 0.00 0.00

Canada 0.01 0.01 0.00 0.00 0.01 0.02 0.04 0.10Japan 0.00 0.00 0.02 0.04 0.03 0.06 0.11 0.17USA 0.02 0.04 0.03 0.13 0.01 0.05 0.07 0.06UK 0.02 0.05 0.01 0.01 0.02 0.04 0.01 0.00

Italy 0.01 0.01 0.00 0.00 0.00 0.00 0.12 0.25

Note: ‘N’, ‘S’ are non-selected and selected. H0: constant = forecasting model;H1: forecasting model is better than the constant; The null hypothesis is rejectedby a p-value smaller than five percent.

When instead of the countries the indicator variables are evaluated most of them are found to

have at least some informational content. With the interest rate measures leading the way, also

UNEMP and CPI have significantly higher QPS and LPS than the corresponding constants. The

forecasting performance of PROD, M1 and M2 is significantly lower but in more than half of the

cases still higher than the constant.

19

The results of the Diebold-Mariano tests broadly support these findings (see table 6). The

all-variable cases exhibit for all countries a p-value of zero indicating that the null of forecasting

model and constant being equal is clearly rejected. Remaining in the country perspective but

turning to the single variable cases, it emerges that the results here differ somewhat from the

previous measures. The Diebold-Mariano framework indicates the best predictability for Germany,

USA and UK which all have the double digit number of below-5-percent p-values. This indeed

differs from the QPS and LPS measures since their results suggested that Japan was the country

with the best and among others Germany and UK, the countries with the least predictable stock

markets. When taking on the perspective of the single indicator variables the results are more

similar. It can be seen that short (IB) and long term (GB) interest rates as well as their difference,

the SPREAD variable, exhibit the lowest p-values among all variables for most of the countries.

Hence, this indicates that the models with the best forecasting performances are based on interest

rates measures.

3.2.2 Out-of-Sample Analysis

To evaluate the prediction power of the indicator variables under more realistic conditions, we

employ an out-of-sample analysis. From now on, the sample is divided in two parts: An estimation

period, where the coefficient estimates are obtained and an out-of-sample period, where the predicted

probabilities are computed and evaluated against the realized data points. In the baseline set-up

January 1990 was selected as the date that separates both periods. This point in time is changed

in the robustness section to 1995 and 2000 with the intention to cope with the trade-off between a

longer estimation period, which delivers more reliable coefficients and a longer evaluation sample that

facilitates the assessment of the forecasting power. To furthermore construct realistic forecasting

conditions, we set the minimum lag length to three lags, since all indicator variables used in this

analysis are publicly available to forecasters within a three month range.

For the preliminary analysis, again the predicted probabilities are graphed against the time

(figure 4). At a first glance, it seems that the fitted values meet the bear market series less accurately

than in the in-sample case. As an example the case of Canada might serve, where the probabilities

drift persistently to the right without any change during recession times. Furthermore, the 0-1-

pattern in France and Italy as well as to some extent in the UK is striking. This is due to the

fact that the missing indicator variables in the beginning of the estimation sample are still feeding

through after some time.

Since in the out-of-sample analysis, the pseudo R2 ist not applied, we immediately turn to

20

Figure 4: Out-of-sample recession probabilities - all variables - 3 lags

Germany

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 20080.00

0.25

0.50

0.75

1.00

France

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 20080.00

0.25

0.50

0.75

1.00

Canada

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 20080.00

0.25

0.50

0.75

1.00

Japan

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 20080.00

0.25

0.50

0.75

1.00

USA

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 20080.00

0.25

0.50

0.75

1.00

United Kingdom

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 20080.00

0.25

0.50

0.75

1.00

Italy

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 20080.00

0.25

0.50

0.75

1.00

Note: shaded part = actual bear markets; plotted line = fitted values of the probit estimation

the QPS and LPS analysis. In the all-variable case for all countries, the corresponding QPS and

LPS measures are consequently lower than the constant indicating that there is no improvement

by using all indicator variables for forecasting (see table 7 and 7). Closest to the constant are the

variable values of Canada (0.46 (QPS), 0.79 (LPS)) with constants of 0.39 and 0.58 respectively.

In contrast, the lowest prediction power is exhibited in the all-variable specifications for France

and Italy, with exemplary values for the French measures of 0.76 (QPS) and 12.15 (LPS) and

corresponding constants of 0.43 and 0.63.

When examining the country perspective for the single variable case, the following picture

emerges. According to QPS and LPS, the best predictions can be made for the stock markets

downturns in the UK, Italy and Japan - here, a large number of indicator variables have a lower

QPS and LPS than the constant. In constrast to these findings, the US market shows no signs

of predictability at all, with only one indicator variable being useful (M2 in the LPS results). For

the markets of Germany, France and Canada the results are ambiguous, since in each case at least

21

two indicator variables have more predictive power than the constant. But the downturns are less

predictable than in the UK and Japan.

Table 7: Out-of-sample results 1990 - QPS - 3 lags





Note: ‘N’, ‘S’ are non-selected and selected. In the selected estimation are thesignificant parameters of the 12 lags non-selected estimation included. ‘Const’ isthe Constant which is used as a benchmark for evaluating the forecasting abilitiesof the exogenous variables (bold figures = smaller than the constant).

Table 8: Out-of-sample results 1990 - LPS - 3 lags


Germany 1.39 1.09 0.58 0.57 0.66 0.72 0.54 0.55 1.22 1.28France 12.15 1.82 0.70 0.70 0.66 0.65 0.67 0.63 0.80 0.66Canada 0.79 0.67 0.59 0.58 0.61 0.61 0.59 0.58 0.59 0.58Japan 1.72 1.17 0.85 0.85 0.88 0.85 0.84 0.82 0.85 0.83USA 1.14 0.91 0.70 0.69 0.67 0.67 0.69 0.71 0.67 0.65

UK 6.65 1.88 0.60 0.60 0.62 0.61 0.60 0.60 0.82 0.85Italy 4.99 7.17 0.69 0.69 0.68 0.68 0.70 0.71 0.74 0.71




Changing the perspective and proceeding with an assessment of the different indicator variables,

it can be clearly stated that the variables with the highest prediction power are among the interest

rate measures. UNEMP, however, shows in most cases a significantly high prediction power as well.

22

Table 9: Diebold Mariano Test of the out-of-sample results 1990 - 3 lags (p-values)




Germany 0.65 0.64 0.69 0.59 0.84 0.59 0.38 0.19France 0.95 0.90 0.88 0.86 0.95 0.74 0.02 0.01

Canada 0.67 0.40 0.86 0.81 0.15 0.11 1.00 0.99Japan 0.04 0.02 0.39 0.27 0.25 0.18 0.97 0.89USA 0.99 0.96 0.97 0.79 0.89 0.86 1.00 1.00UK 0.12 0.11 0.00 0.00 0.21 0.17 0.25 0.07Italy 0.38 0.03 0.15 0.01 0.82 0.46 1.00 0.95


At least for half of the countries, most QPS and LPS values in these categories, are smaller than

those of the constant. The other indicator variables exhibit fairly less informational content and

therefore have in most cases a higher QPS and LPS than the corresponding constant. The only

notable exception is Italy, where according to all measures CPI indicates good prediciton qualities.

Turning here as well to the results of the Diebold-Mariano test, it is striking that the number of

forecasting models that are significantly better than the constant is somewhat lower than indicated

by the other measures (see table 9). Promising forecasts however can be made for France with the

UNEMP, for Japan with IB, and for the UK with GB. However, the high number of positive QPS

and LPS results for the UK seems to be largely insignificant. Furthermore, in the case of Italy, the

selection procedure in both interest rate cases delivers a good forecasting model.

3.2.3 Robustness Check

In addition to the estimations undertaken in the last two subsections, we also check for the sensitivity

of our results to a later starting point in the out-of-sample analysis as well as for variations in the

identification procedure for bull and bear markets.

We first set the starting point for the out-of-sample analysis to January 1995 - see table 11-13

in the appendix - and later on to January 2000 (table 14-16). The findings organized by countries

can be summerized as follows: Based on the already high prediction power of the 1990-sample, the

QPS and LPS values for the indicator variables of Japan and Italy are often significantly higher

23

than the corresponding values of the constant. On the other side of the spectrum, the US are the

country whose stock market downturns are least predictable. In basically all cases, the US indicator

variables were not able to beat the predictions made by the constant. A similar point can be stated

for Canada, yet with a reservation on the LPS case for 1995, where a larger number of inidicator

variables contains some prediction power. However, the difference to the LPS in the 1990-sample is

very small for most variables of Canada. While the UK seems to have a high informational content

in the 1990-sample, the number of cases, where the QPS and LPS of the indicator variables are

smaller than the ones for the constant, decreases over time. Finally, in the 2000-sample for the UK

only a few cases with good prediction power remained. Germany and France undergo development

in the opposite direction. Both countries show a rather low prediction power in the 1990-sample

with only two values of the QPS beating the constant. For 1995 in the case of Germany and 2000 in

the one of France, both countries show clear signs of bear market predictability. Nevertheless, the

high forecasting power for Germany is reduced somewhat in the 2000-sample.

When the presentation of the out-of-sample results is organzied by indicator variables, the above

derived pattern, with interest rate variables and UNEMP being the best predictors for stock market

downturns is largely conmfired in the 1995- and the 2000-sample. For the 1995-sample, GB seems

to have a slightly exposed position as the very best predictor just like IB in the 2000-sample. In

contrast, the other indicator variables barely beat the constant. Exemptions are again Italy, whose

CPI value constantly indicates high predictive power and the two money supplies - predominantly

M1 - for Germany and Japan which also exhibit some informational content.

The Diebold-Mariano results generally support the above mentioned findings. The highest

number of models that perform significantly better than the constant is found for Germany, France,

and Italy under both out-of-sample starting points. Countries such as the USA, UK and Canada, as

well as to some extent Japan have much higher p-values than the 5-percent level, implying that the

forecasting models cannot beat the model with only a constant. Taking on the indicator variable

perspective, it is shown again that interest rate variables and UNEMP have the highest chances

to beat the constant. However, when applying the Diebold-Mariano test to both out-of-sample

starting points, it turns out that SPREAD and UNEMP seem to be the only variables that beat

the constant in larger number of countries. These findings differ to some extent from the results of

previous measures such as QPS and LPS, which assigned a high prediction power to all kinds of

interest rate variables.

To check for robustness against the criteria of the bear market identification process, we change

the minimum phase length of a bull or bear market from four to eight months. As expected, this

24

step reduces the number of bear markets somewhat and increases the period between two turning

points.

The in-sample results for the one lag length under the increased minimum phase length are

broadly similar to the former results.10 For the pseudo R2, QPS and LPS most values are on largely

similar levels and in some cases did not change at all. Interestingly, as QPS and LPS values suggest,

a considerable number of values even seem to be consistently smaller by a certain margin. Hence,

this shows that an increase in the minimum phase length improves the forecasting performance of

the indicator variables instead of decreasing it. Therefore, keeping the minimum phase length at

the originally selected four month is a rather cautious approach.

The out-of-sample results confirm these findings as well, when the longer minimum phase length

requirement is applied to the out-of-sample specifications. The QPS values are again largely in line

with the original results and whenever a difference ocurrs, the prediction power has increased, rather

then diminished. For the LPS, the number of specifications with high informational content is lower

and a few earlier values have changed. However, since countries whose stock market downturns were

forecastable best and worst in the 1990-sample have remained the same. In place of the indicator

variables, interest rates and UNEMP still exhibit the highest prediction power. The four months

phase length seems thoroughly feasible.

3.3 Conclusion

The goal of this paper was to evaluate a set of macroeconomic indicator variables with respect to

its prediction power on stock market downturns in G7 countries. The applied methodical approach

consisted of two steps. At first, a modified version of the Bry-Boschan business cycle dating algorithm

was applied to identify bull and bear markets from the data by creating dummy variable series. In

a second step, under an in-sample and out-of-sample framework, probit estimations were carried

out by regressing the newly identified dummy variable series on different specifications of indicator

variables. To assess the hereby generated estimation results, typical forecasting evaluation measures

were employed. Especially three findings have emerged from this analysis:

Firstly, in the in-sample analysis, the all-variable specifications, i.e. those including all indicator

variables of the set, show the highest prediction power across all countries. In the out-of-sample

analysis, this is not longer the case, since predictions made by single variables and its lagged values

yield significantly better forecasts.

Secondly, when seen from the countries’ perspective, stock market downturns can be predicted

best for Japan, Italy, and to a lower extent for France and Germany. The countries with the least

10Tables are not reported but available on request.

25

predictable downturns were the US, Canada and the UK in more recent times. As an explanation

for these findings could serve the fact that Anglo-American countries - who are all in the group with

the less predictive marekts - have adopted maket based systems to conduct financial intermediation.

As a result, the stock markets of these countries are large and deep. Indeed, when comparing the

market capitalization of listed companies in percent of GDP for 2006, the UK (160 percent), the

USA (148), and Canada (134) show significantly higher ratios than Japan and France (each 108) as

well as Germany (57) and Italy (55).11 Hereby, the market size could make the stock markets more

informationally efficient - e.g. by creating a larger base of informed investors, stronger disclosure

standards, or broader media coverage - and hence reduce the possibility to obtain good forecasts.

In contrast, the banking system orientated European countries, such as Germany, Italy, France, and

Japan might have relatively less developed stock markets, a lower degree of market efficiency and

hence, better predictable stock prices.

Thirdly, macroeconomic indicator variables with the best prediction power in in- and out-of-

sample are especially the interest rates and their linear combination - the term spread - and the

unemployment rate. Prices follow thereafter. Finally, the least prediction power is found in the

two money stock series. A possible reason for this observation could be that monetary authorities

usually act not till the stock market downturn becomes severe and hence, the money stock variables

only contain little informational content. However, the companies might act somewhat earlier and

could sporadically adjust production and lay off workers before the stock market downturn sets in.

In accordance with the literature, the interest rate based variables exhibit the highest prediction

power of all variables in our analysis as well. A possible explanation for this result could be given

by the fact that interest rates contain a risk premium, which doublessly increases, when a crisis

approaches.

Referring to the purposes that this study should fulfill, besides its academic contribution, one

can exploit its value for the two other target groups: For policy makers, the recommendation might

be that an analysis of interest rates is a good point to start with, when the risk of a stock market

downturn is assessed. For investors, the answer is somewhat more complex. According to our findings

investors are advised to carefully examine interest rates. Furthermore, investments in the Japanese

and Italian markets seem to yield the most non-random returns. However it should be noted that

when investors decide to reallocate their investments, a certain ammount of transaction costs occurs.

To examine the practical value of the here derived results, assumptions about these transaction costs

and the investment’s opportunity costs have to be made in the first place. Moreover, a personal

threshold depending on each investor’s preferences that indicates when the investor should exit the

11World Development Indicators

26

market has to be determined as well.

Possible lines of future research may also include: A comparison of different identification pro-

cedures for the bear market series - such as in Chen [2009], who identified the turning points via

a Markov-switching model. Furthermore, the lag structure of the best specifications could be ex-

tracted and subjected to further tests. Finally, it would be interesting to see how other indicator

variables, such as business or consumer sentiment indices, developments in commodity prices, and

typical financial risk measures score in this assessment.

27

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30

Appendices

Table 10: Mean and standard deviation of the log-MSCI series

Mean Standard DeviationGermany 5.75 0.99France 6.17 1.1Canada 5.91 0.86Japan 6.23 0.77US 5.4 0.84UK 5.88 1.1Italy 5.71 1.2



Germany 0.52 0.34 0.40 0.39 0.38 0.41 0.46 0.46 0.49 0.46France 0.78 0.59 0.49 0.49 0.46 0.46 0.48 0.46 0.50 0.45

Canada 0.37 0.32 0.34 0.33 0.34 0.34 0.34 0.33 0.33 0.33Japan 0.63 0.60 0.58 0.59 0.59 0.58 0.55 0.53 0.57 0.55

USA 0.55 0.50 0.53 0.51 0.48 0.47 0.48 0.48 0.48 0.46UK 0.53 0.40 0.42 0.42 0.43 0.42 0.42 0.42 0.47 0.47Italy 0.73 0.57 0.50 0.50 0.48 0.48 0.50 0.52 0.54 0.50




31



Germany 0.97 0.52 0.59 0.58 0.63 0.69 0.54 0.55 1.32 1.41France 5.93 1.62 0.72 0.71 0.67 0.67 0.69 0.65 0.74 0.64

Canada 0.57 0.50 0.53 0.52 0.53 0.53 0.52 0.52 0.51 0.52Japan 0.91 0.84 0.78 0.79 0.80 0.78 0.74 0.72 0.77 0.75USA 0.94 0.82 0.73 0.71 0.67 0.67 0.68 0.70 0.68 0.65UK 2.31 2.01 0.62 0.61 0.63 0.61 0.62 0.61 0.69 0.68Italy 1.28 0.84 0.69 0.69 0.67 0.68 0.69 0.71 0.73 0.70






Germany 1.00 0.02 0.97 0.48 0.41 0.88 0.98 0.99 1.00 0.99France 1.00 0.97 0.95 0.95 0.70 0.49 1.00 0.02 1.00 0.02



Germany 0.00 0.00 0.33 0.29 0.00 0.00 0.14 0.09France 0.94 0.90 0.90 0.86 0.52 0.37 0.00 0.00


Italy 0.08 0.07 0.06 0.01 0.01 0.00 0.96 0.09


32




USA 0.73 0.66 0.59 0.57 0.59 0.58 0.68 0.68 0.57 0.54

UK 0.74 0.60 0.58 0.56 0.61 0.60 0.58 0.56 0.63 0.62Italy 0.80 0.65 0.50 0.50 0.50 0.50 0.53 0.53 0.53 0.50







USA 1.25 1.10 0.79 0.77 0.79 0.78 0.94 0.96 0.77 0.73

UK 1.52 3.09 0.80 0.77 0.84 0.82 0.80 0.77 0.87 0.86Italy 1.20 0.91 0.69 0.69 0.69 0.69 0.73 0.73 0.72 0.69




33



Germany 1.00 0.85 0.75 0.02 1.00 1.00 0.64 0.84 0.63 0.02

France 1.00 0.50 0.89 0.89 0.68 0.50 1.00 0.02 1.00 0.02



Germany 0.43 0.44 0.98 0.98 0.00 0.00 0.99 0.99France 0.23 0.20 0.18 0.23 0.54 0.48 0.00 0.00


Italy 0.18 0.63 0.99 0.94 0.00 0.00 1.00 0.39


34

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On the Look-Out for the Bear: Predicting Stock Market ... · minimum stock market cycle length is at least sixteen months. This is only a slight modi ca-tion of the 15-months minimum